Q: Does the Holographic Projector make it as though I own other people’s Keepers, and can use their powers, or just for meeting the Goal?

A: The Holographic Projection / Hologram card clearly says you can WIN with Keepers owned by other players. This means it’s power works with respect to the win conditions only. There’s nothing there about it being able to mimic the special powers of those other Keepers. I can’t use a hologram of your Doctor to cure my crewperson of Brain Parasites.